/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        arm_spline_interp_f32.c
 * Description:  Floating-point cubic spline interpolation
 *
 * $Date:        13 November 2019
 * $Revision:    V1.6.0
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "arm_math.h"

/**
  @ingroup groupSupport
 */

/**
  @defgroup SplineInterpolate Cubic Spline Interpolation

  Spline interpolation is a method of interpolation where the interpolant
  is a piecewise-defined polynomial called "spline".

  @par Introduction

  Given a function f defined on the interval [a,b], a set of n nodes x(i)
  where a=x(1)<x(2)<...<x(n)=b and a set of n values y(i) = f(x(i)),
  a cubic spline interpolant S(x) is defined as:

  <pre>
          S1(x)       x(1) < x < x(2)
  S(x) =   ...
          Sn-1(x)   x(n-1) < x < x(n)
  </pre>

  where

  <pre>
  Si(x) = a_i+b_i(x-xi)+c_i(x-xi)^2+d_i(x-xi)^3    i=1, ..., n-1
  </pre>

  @par Algorithm

  Having defined h(i) = x(i+1) - x(i)

  <pre>
  h(i-1)c(i-1)+2[h(i-1)+h(i)]c(i)+h(i)c(i+1) = 3/h(i)*[a(i+1)-a(i)]-3/h(i-1)*[a(i)-a(i-1)]    i=2, ..., n-1
  </pre>

  It is possible to write the previous conditions in matrix form (Ax=B).
  In order to solve the system two boundary conidtions are needed.
  - Natural spline: S1''(x1)=2*c(1)=0 ; Sn''(xn)=2*c(n)=0
  In matrix form:

  <pre>
  |  1        0         0  ...    0         0           0     ||  c(1)  | |                        0                        |
  | h(0) 2[h(0)+h(1)] h(1) ...    0         0           0     ||  c(2)  | |      3/h(2)*[a(3)-a(2)]-3/h(1)*[a(2)-a(1)]      |
  | ...      ...       ... ...   ...       ...         ...    ||  ...   |=|                       ...                       |
  |  0        0         0  ... h(n-2) 2[h(n-2)+h(n-1)] h(n-1) || c(n-1) | | 3/h(n-1)*[a(n)-a(n-1)]-3/h(n-2)*[a(n-1)-a(n-2)] |
  |  0        0         0  ...    0         0           1     ||  c(n)  | |                        0                        |
  </pre>

  - Parabolic runout spline: S1''(x1)=2*c(1)=S2''(x2)=2*c(2) ; Sn-1''(xn-1)=2*c(n-1)=Sn''(xn)=2*c(n)
  In matrix form:

  <pre>
  |  1       -1         0  ...    0         0           0     ||  c(1)  | |                        0                        |
  | h(0) 2[h(0)+h(1)] h(1) ...    0         0           0     ||  c(2)  | |      3/h(2)*[a(3)-a(2)]-3/h(1)*[a(2)-a(1)]      |
  | ...      ...       ... ...   ...       ...         ...    ||  ...   |=|                       ...                       |
  |  0        0         0  ... h(n-2) 2[h(n-2)+h(n-1)] h(n-1) || c(n-1) | | 3/h(n-1)*[a(n)-a(n-1)]-3/h(n-2)*[a(n-1)-a(n-2)] |
  |  0        0         0  ...    0        -1           1     ||  c(n)  | |                        0                        |
  </pre>

  A is a tridiagonal matrix (a band matrix of bandwidth 3) of size N=n+1. The factorization
  algorithms (A=LU) can be simplified considerably because a large number of zeros appear
  in regular patterns. The Crout method has been used:
  1) Solve LZ=B

  <pre>
  u(1,2) = A(1,2)/A(1,1)
  z(1)   = B(1)/l(11)

  FOR i=2, ..., N-1
    l(i,i)   = A(i,i)-A(i,i-1)u(i-1,i)
    u(i,i+1) = a(i,i+1)/l(i,i)
    z(i)     = [B(i)-A(i,i-1)z(i-1)]/l(i,i)

  l(N,N) = A(N,N)-A(N,N-1)u(N-1,N)
  z(N)   = [B(N)-A(N,N-1)z(N-1)]/l(N,N)
  </pre>

  2) Solve UX=Z

  <pre>
  c(N)=z(N)

  FOR i=N-1, ..., 1
    c(i)=z(i)-u(i,i+1)c(i+1)
  </pre>

  c(i) for i=1, ..., n-1 are needed to compute the n-1 polynomials.
  b(i) and d(i) are computed as:
  - b(i) = [y(i+1)-y(i)]/h(i)-h(i)*[c(i+1)+2*c(i)]/3
  - d(i) = [c(i+1)-c(i)]/[3*h(i)]
  Moreover, a(i)=y(i).

 @par Behaviour outside the given intervals

  It is possible to compute the interpolated vector for x values outside the
  input range (xq<x(1); xq>x(n)). The coefficients used to compute the y values for
  xq<x(1) are going to be the ones used for the first interval, while for xq>x(n) the
  coefficients used for the last interval.

 */

/**
  @addtogroup SplineInterpolate
  @{
 */

/**
 * @brief Processing function for the floating-point cubic spline interpolation.
 * @param[in]  S          points to an instance of the floating-point spline structure.
 * @param[in]  xq         points to the x values ot the interpolated data points.
 * @param[out] pDst       points to the block of output data.
 * @param[in]  blockSize  number of samples of output data.
 */

void arm_spline_f32(
	arm_spline_instance_f32 *S,
	const float32_t *xq,
	float32_t *pDst,
	uint32_t blockSize)
{
	const float32_t *x = S->x;
	const float32_t *y = S->y;
	int32_t n = S->n_x;

	/* Coefficients (a==y for i<=n-1) */
	float32_t *b = (S->coeffs);
	float32_t *c = (S->coeffs) + (n - 1);
	float32_t *d = (S->coeffs) + (2 * (n - 1));

	const float32_t *pXq = xq;
	int32_t blkCnt = (int32_t)blockSize;
	int32_t blkCnt2;
	int32_t i;
	float32_t x_sc;

#ifdef ARM_MATH_NEON
	float32x4_t xiv;
	float32x4_t aiv;
	float32x4_t biv;
	float32x4_t civ;
	float32x4_t div;

	float32x4_t xqv;

	float32x4_t temp;
	float32x4_t diff;
	float32x4_t yv;
#endif

	/* Create output for x(i)<x<x(i+1) */
	for (i = 0; i < n - 1; i++) {
#ifdef ARM_MATH_NEON
		xiv = vdupq_n_f32(x[i]);

		aiv = vdupq_n_f32(y[i]);
		biv = vdupq_n_f32(b[i]);
		civ = vdupq_n_f32(c[i]);
		div = vdupq_n_f32(d[i]);

		while (*(pXq + 4) <= x[i + 1] && blkCnt > 4) {
			/* Load [xq(k) xq(k+1) xq(k+2) xq(k+3)] */
			xqv = vld1q_f32(pXq);
			pXq += 4;

			/* Compute [xq(k)-x(i) xq(k+1)-x(i) xq(k+2)-x(i) xq(k+3)-x(i)] */
			diff = vsubq_f32(xqv, xiv);
			temp = diff;

			/* y(i) = a(i) + ... */
			yv = aiv;
			/* ... + b(i)*(x-x(i)) + ... */
			yv = vmlaq_f32(yv, biv, temp);
			/* ... + c(i)*(x-x(i))^2 + ... */
			temp = vmulq_f32(temp, diff);
			yv = vmlaq_f32(yv, civ, temp);
			/* ... + d(i)*(x-x(i))^3 */
			temp = vmulq_f32(temp, diff);
			yv = vmlaq_f32(yv, div, temp);

			/* Store [y(k) y(k+1) y(k+2) y(k+3)] */
			vst1q_f32(pDst, yv);
			pDst += 4;

			blkCnt -= 4;
		}
#endif
		while (*pXq <= x[i + 1] && blkCnt > 0) {
			x_sc = *pXq++;

			*pDst = y[i] + b[i] * (x_sc - x[i]) + c[i] * (x_sc - x[i]) * (x_sc - x[i]) + d[i] * (x_sc - x[i]) * (x_sc - x[i]) * (x_sc - x[i]);

			pDst++;
			blkCnt--;
		}
	}

	/* Create output for remaining samples (x>=x(n)) */
#ifdef ARM_MATH_NEON
	/* Compute 4 outputs at a time */
	blkCnt2 = blkCnt >> 2;

	while (blkCnt2 > 0) {
		/* Load [xq(k) xq(k+1) xq(k+2) xq(k+3)] */
		xqv = vld1q_f32(pXq);
		pXq += 4;

		/* Compute [xq(k)-x(i) xq(k+1)-x(i) xq(k+2)-x(i) xq(k+3)-x(i)] */
		diff = vsubq_f32(xqv, xiv);
		temp = diff;

		/* y(i) = a(i) + ... */
		yv = aiv;
		/* ... + b(i)*(x-x(i)) + ... */
		yv = vmlaq_f32(yv, biv, temp);
		/* ... + c(i)*(x-x(i))^2 + ... */
		temp = vmulq_f32(temp, diff);
		yv = vmlaq_f32(yv, civ, temp);
		/* ... + d(i)*(x-x(i))^3 */
		temp = vmulq_f32(temp, diff);
		yv = vmlaq_f32(yv, div, temp);

		/* Store [y(k) y(k+1) y(k+2) y(k+3)] */
		vst1q_f32(pDst, yv);
		pDst += 4;

		blkCnt2--;
	}

	/* Tail */
	blkCnt2 = blkCnt & 3;
#else
	blkCnt2 = blkCnt;
#endif

	while (blkCnt2 > 0) {
		x_sc = *pXq++;

		*pDst = y[i - 1] + b[i - 1] * (x_sc - x[i - 1]) + c[i - 1] * (x_sc - x[i - 1]) * (x_sc - x[i - 1]) + d[i - 1] * (x_sc - x[i - 1]) * (x_sc - x[i - 1]) *
				(x_sc - x[i - 1]);

		pDst++;
		blkCnt2--;
	}
}

/**
  @} end of SplineInterpolate group
 */
